Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is

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Solution

Q.
Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is (in pF) [2025]

1 600

2 200

3 400

4 100

Ans.
(2)

New potential $= \frac{C_{0} V_{0}}{C_{0} + C} = \frac{V_{0}}{3}$

$3 C_{0} V_{0} = C_{0} V_{0} + C V_{0}$

$2 C_{0} V_{0} = C V_{0}$

$C = 2 C_{0} = 2 \times 100 = 200 pF$

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